Line lens and method of design therefor

ABSTRACT

An improved line lens for producing output radiation in the form of a narrow sheet from a collimated input beam despite the use of a lens material having an index of refraction of less than 1.6. A novel design method permits redistribution of output energy as a function of angle along the surface of the lens to achieve the specified output pattern and defines the polynomials of the contoured surface curves of such a lens. In one embodiment of such a lens, which is designed by the inventive method, the input shape is contoured by circular segments and the exit surface is contoured according to the design-method-produced polynomials.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention pertains generally to the field of optical lensesand more specifically, to a line lens or beam spreader lens forconverting a narrow, round beam of radiation into a uniformly dispersedsheet of radiation.

2. Prior Art

A lens which converts a narrow, round beam of radiation into a uniformlydistributed sheet of radiation finds its principal usefulness inmilitary applications such as laser scan radar. It is well-known that around beam of radiation when passed through a cylindrically curvedrefracting surface will be dispersed into a sheet of radiation. However,a number of critical deficiencies are encountered. For example, the spanor width of the sheet obtained from practical curvatures of therefracting surface is inadequate in that it does not satisfy the normalrequirement for a 90 degree span. Furthermore, if the curvature of thecylinder is sufficiently high, portions of the beam incident on the highangle regions of the surface are severely attenuated and in fact,radiation gaps are produced because the critical angle for totalinternal reflection will be exceeded for certain portions of thesurface. As a result, a relatively non-uniform radiation pattern isproduced which may in fact, comprise a plurality of non-radiationregions interspersed therethrough. Still an additional problemencountered in attempting to use a cylindrically curved refractingsurface to generate a sheet of radiation from an incident beam, resultsfrom the awkward mechanical problems associated with the attempt toconcentrate the incident beam over the span of the lens.

A prior art beam spreader lens has overcome the aforementioned problemsof a cylindrically curved refracting surface. More specifically, a priorart lens having lenticular elements that are alternately concave andconvex has been developed out of an extremely high index of refractionmaterial (LASF9 having an index of refraction of 1.85). The extremelyhigh index of refraction appears to solve the first two of theaforementioned disadvantages of the cylindrically curved refractingsurface in that the span or width of the radiation sheet obtained fromthis prior art lens appears to be substantially adequate and relativelyuniform without any severely attenuated segments. Furthermore, thelenticular configuration of the lens appears to overcome theaforementioned centration problem wherein a centrally directed incidentbeam is all that is required. Unfortunately, the prior art lensintroduces a significant new disadvantage particularly in certainmilitary applications where a lens of this type finds its mostadvantageous application. More specifically, the exposure of theaforementioned prior art lens to any form of heating, darkens thematerial and changes its optical characteristics rendering itstransmission capabilities inadequate for the purpose to which it isapplied. For example, in some applications the lens is exposed toatmosphere in a high velocity flight vehicle and in such applications,the air resistance is sufficient to heat the lens to an extent that theaforementioned detrimental optical characteristic changes occur.Consequently, the aforementioned high index of refraction material isnot available for use as a line lens wherever that lens may be heated inits application.

there is however a far more suitable material available, namely, glassceramic sold under such trademarks as ZERODUR and CERVIT. Such glassceramic is resistant to heating in that it does not substantially changeits transmission or other optical characteristics as a result ofsignificantly higher temperatures. Unfortunately, ZERODUR for examplehas an index of refraction of only 1.544. As a result, the lensstructure and geometry utilized to produce the prior art line lens usingthe aforementioned high index of refraction material, would not producethe same uniformly distributed 90 degree sheet beam in a line lensmanufactured from glass ceramic. Consequently, the problem to be solvedby the present invention is to provide a line lens which takes advantageof the aforementioned prior art line lens to the extent that itcontinues to satisfy the requirements of uniform sheet radiationdistribution over a 90 degree field with a structural configuration thatmay be readily produced and at the same time permit the use of glassceramic which will resist the aforementiond heating effect inducedproblems despite the significantly lower index of refraction compared tothe prior art material discussed above.

SUMMARY OF THE INVENTION

The present invention comprises a novel line lens for producingradiation in the form of a sheet from a collimated round pencil beam ofsuch radiation. The radiation span or width is a minimum of 90 degreesand the radiation pattern is substantially uniform over the 90 degreeangle. Furthermore, the lens utilizes the advantageous lenticularconstruction of the prior art to overcome construction problemsassociated with centration of the beam over the lens surface.Furthermore, the present invention utilizes a novel design to permitachievement of the aforementioned desirable characteristics despite thefact that the material of which the lens is constructed is a glassceramic having an index of refraction of 1.544, significantly lower thanLASF9 but without the attendant heat-induced degradation of opticalcharacteristics. One line lens embodiment of the present inventionachieves the aforementioned advantageous operation by a double powersurface element configuration in which both the light incident surfaceand the light exiting or transmission surface are lenticulated. Bothlens surfaces are lenticulated and the lenticulation curve design of onesurface is dependent upon the lenticulation curve design of the other.It will be seen hereinafter that the resultant structure of the lens isachieved by a novel design method which is relatively unique as comparedto conventional optical lens design techniques.

OBJECTS OF THE INVENTION

It is therefore a principal object of the present invention to provide aline lens for producing radiation in the form of a sheet from acollimated round pencil beam wherein despite the index of refraction ofthe lens material being no greater than 1.544, the resultant radiationsheet spans an angle of at least 90 degrees and is substantially uniformover that span.

It is an additional object of the present invention to provide a noveldesign method for calculating the geometrical surfaces of a doublylenticulated line lens that is capable of producing a sheet of radiationof uniform distribution over an angle of approximately 90 degrees usingmaterials having an index of refraction in the range of 1.45 to 1.6.

It is still an additional object of the present invention to provide aline lens capable of producing a sheet of radiation from a collimatedpencil beam wherein the radiation is uniform over an angle ofapproximately 90 degrees utilizing glass ceramic material and a uniquelyconfigured lenticulated surface on each side of the lens to produce adouble power surface element.

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned objects and advantages of the present invention aswell as additional objects and advantages thereof will be more fullyunderstood hereinafter as a result of a detailed description of apreferred embodiment of the invention when taken in conjunction with thefollowing drawings in which:

FIG. 1 is an elevational view of the desired radiation pattern producedby the present invention in response to a source beam incident on theline lens of the invention;

FIG. 2 is a side view of the radiation pattern produced by the inventionas illustrated in FIG. 1;

FIG. 3 is a graph illustrating the internal reflection characteristicsof a suitable material for producing the line lens of the presentinvention;

FIG. 4 is a graphical illustration of the construction details used forcomputing the lenticular surface contours of a line lens of the presentinvention;

FIGS. 5 and 6 are graphical illustrations of various curves used in thedesign calculations of the lenticular surface contours of the line lensof the present invention;

FIGS. 7, 8 and 9 are enlarged views side and front respectivelyillustrating the structure details of the line lens of the presentinvention; and

FIGS. 10 to 12 provide views of various apparatus used in themanufacture of the lens of the present invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

Reference will now be made to FIGS. 1, 2 and 3 for a more preciseindication of the performance of a line lens or beam spreader lensembodiment of the invention. More specifically, as seen in FIG. 1, anembodiment 10 of the beam spreader lens of the present inventionreceives a source beam in the form of a collimated beam of approximately2 millimeters in diameter. It will be understood that the source beamprecise shape and dimension is not limitative of the invention. The beamspreader lens 10 of the present invention operates on this incidentsource beam to produce an output radiation beam 6 shown in FIG. 1.Ideally, the output radiation pattern should comprise a 90 degree wedgethat is symmetrical with respect to the normal center line of the lensand is substantially uniform in intensity over the entire spread of thewedge pattern. As seen further in FIG. 1, the actual specification forthe output radiation pattern of the lens 10 of the invention permits acertain degree of variation from this ideal pattern as indicated by thetolerance boundaries 7 and 8 which represent permissible intensityvariation and which include a designed-in up to 10 percent increase inintensity 9 at wedge angles approaching the outer limits of the beamat + or -45 degrees from the normal to the lens.

For purposes of explanation only, FIG. 1 includes a display target 12 inthe form of a rectangle curved to conform to the shape of a portion of acircular rim. Target 12 is seen in side view in FIG. 2 to illustrate thecross sectional representations of the incident source beam 5, the beamspreader lens 10 and the output radiation pattern 6 as it intersects thetarget 12. Further specifications for the lens 10 of the presentinvention require that the lens be made of a glass ceramic material aspreviously discussed. Furthermore, although it will be seen hereinafterthat both surfaces of the lens are lenticulated, the nominal thicknessor spacing between the refractive surfaces is approximately 1/10 of aninch and the lens has a diameter of approximately 1/2 of an inch,although these dimensions should not be considered limitative of theinvention.

Those having skill in the art to which the present invention pertainswill appreciate the fact that in order to design a line lens from aglass ceramic material such as ZERODUR, which has an index of refractionof 1.544, significantly lower than the material LASF 9 previouslyalluded to, it is necessary to know the material's internal reflectioncharacteristics. It is of particular importance in a view of the angularbends of up to 45 degrees for the incoming source beam as seen in FIG. 1to know the reflection characteristics of the exiting surface as afunction of various angles of incidence. Before the detailed designprocess commences we must know the angle limitations due to thematerial's reflection characteristics. For this reason reference willnow be made to FIG. 3 which comprises a graph showing the reflectioncharacteristics of the exiting surface of a ZERODUR lens. As seen inFIG. 3 there are two curves of reflection characteristics illustrated,one for the plane of polarization parallel to the plane of incidence andone for the plane of polarization normal to the plane of incidence. Thelimitations dictated by the reflection characteristics as indicated inFIG. 3 have implications on the design of the lens as will be seenhereinafter. As previously indicated, prior art beam spreader lenseswere able to achieve an angular beam spread of 90 degrees by using aglass of high index of refraction of approximately 1.8. Because of thishigh index of refraction and the concomitant high angle of totalinternal reflection, a prior art lens design utilizing a singlelenticulated surface could be achieved because the surface curvaturescould be sufficiently high to achieve the 90 degree beam spread.However, because of the substantially lower index of refraction of glassceramic, surface curvature must be limited to a value which will keepthe angle of incidence at the interfaces below about 35 degrees. Higherangles will result in unacceptable transmission losses. As a result, itwas clearly necessary to use a double surface refractor to achieve thewider beam spread result with the lower index of refraction. Thus thepresent invention comprises a double power surface element in which bothsides of the lens are lenticulated.

While those having skill in the present art will at once see the clearnecessity for using two surfaces with optical power, the means by whichthe design of such surface curvatures is accomplished is not immediatelyapparent. In fact, conventional optical computer programs and prescribeddesign techniques of the prior art have been found inadequate and aunique new design approach was required to produce a successful designof a beam spread lens using a relatively low index of refractionmaterial. This new unique design approach will now be described inconjunction with FIGS. 4, 5 and 6. Referring first to FIG. 4, it will beseen that this figure comprises 100 to 1 scale drawing of a section of abeam spread lens and traces the path of a pair of boundary rays A and B.Only one pair of lenticulations is shown in cross section. This pair istypical of several pairs of lenticulations which comprise the beamspread lens. Each lenticulation covers a span which is less than thesource beam diameter and there are sufficient lenticulations to morethan cover the full beam diameter of the incident beam source.

Boundary rays A and B establish the angular width of the output sheet ofradiation, namely, + or -45 degrees relative to the incident radiationaxis. Ahead of the lens, the boundary rays are, of course, parallel tothe axis of incident radiation. Within the lens the boundary rays areinclined relative to the lens axis because of the effects of thelenticulations on the input surface. The proportion of bending of theboundary rays at the entering and exiting interface surfaces isestablished partly by trial and error and partly to satisfy certainconditions and limitations. More specifically, it is to be observed thatthe pair of lenticular surfaces are each alternately convex and concave.Each convex and concave adjacent pair has an axis and the axis-to-axisspacing has been tentatively and arbitrarily set at 0.04 inches.

For purposes of simplifying curvature calculations and also foroptimizing the cosmetic appearance of the lens, the initial choice ofinclination angle within the lens was 6.8 degrees and the placement ofthe boundary ray was halfway between the axes with the output angle ofthe boundary rays specified as 45 degrees and the angle of the same raywithin the lens set at 6.8 degrees. These parameters determine the slopeangle of the surface element in the region where the rays intersect thesurface and exit into the target or output space. Using Snell's law ofrefraction, the surface slope angle and the angle of incidence of theray at the exiting point were calculated and are seen in the right-handportion of FIG. 4. These angles represented by the letters X and Y inFIG. 4, respectively, were 32.4 degrees and 39.2 degrees, respectively.The 32.4 degrees for the slope angle of the lenticulated surface wouldbe considered acceptable from the standpoint of fabrication difficulty,but the 39.2 degree angle for the angle of incidence of the ray at theexiting point requires closer scrutiny.

More specifically, again referring to FIG. 3, it is seen that thecritical angle for total internal reflection of the ZERODUR material is43.6 degrees. It is also observed that for an angle of incidence of 1degree less than the cut-off angle of 43.6 degrees, the transmissionpercentage is down 40 percent average for the two polarized componentsof the beam. This is, of course, unacceptable because the requiredperformance specification for the beam spreader lens, as discussedearlier in conjunction with FIG. 1, requires better than 100 percent ofaxial radiation intensity at the 45 degree boundary points. Furtherinspection of FIG. 3 shows that even if conditions are changed so thatthe incidence angle is reduced several degrees, the transmissionpercentage will still be significantly below 100 percent and this figuredoes not include other factors such as decollimation errors and surfacecontour errors which also tend to produce transmission losses at the offaxis regions of the field of output radiation.

Clearly it is necessary to find an alternative way to build up theenergy transmission at the boundaries of the output radiation fieldother than by changing the boundary array configuration itself. It willbe seen hereinafter that an important feature of the present inventioncomprises the method by which the energy build up at the boundaries ofthe output field is accomplished.

Referring once again to FIG. 4 it will be seen that the boundary rayshave been drawn in the three fields, namely, the input field ahead ofthe lens, the field within the lens and the output field. From theboundary rays and the field relative to the lens it is possible tocalculate the slope angles of the surface elements at all points wherethe boundary rays intersect the surfaces. If the normals to each ofthese surface components are not projected onto each lenticulation axis,radii are established from which the surface sections between theboundary elements and the axes may be drawn as circular arcs. If thelenticulation surfaces were contoured to be congruent with thesecircular arcs, the resulting line lens would function to produce a flatsheet of radiation as required, but the radiation intensity patternwould be drastically deficient in energy at and near the boundaries.Accordingly, it is necessary to modify the circular curvatures of theexit surface of the lens point-by-point so that the rays in the outputfield are progressively crowded away from the axes and toward theboundaries. More specifically, each ray originating from an evenlyspaced position in the source beam at the input to the lens is presumedto carry within it an equal amount of energy. Thus the energy density inany portion of the output field is increased as the spacing between therays is reduced. Mathematically the energy density is equal to theinverse of the angular ray spacing.

The resulting surface elements will no longer have a mathematicallycircular curvature, but will instead be curves defined graphically bylayout and mathematically by specific polynomial equations. The designof the novel line lens of the present invention is therefore completewhen these polynomial designed curves are substituted for the circulararcs.

It will be noted hereinafter that in the particular embodiment of theinvention herein disclosed only the exit surface contours of the linelens of the invention are being manipulated and the circular contours ofthe input surface are not changed. It has been found that for theparticular output pattern requirements and the lens material used in theparticular embodiment described, manipulation of the output surfacealone was adequate to produce the desired energy distribution. However,it will be understood that the inventive design of the present inventioncontemplates, when required, manipulation of the input surface as well.In fact, it is expected that the combined action of manipulation of bothsurfaces would produce a more accurate and possibly more exoticradiation pattern. It is also known that many different combinations ofsurface curvatures between the two surfaces would produce the sameradiation pattern and all such surface curvature manipulations carriedout in accordance with the present invention are deemed to becontemplated by the scope of the claims hereinafter set forth.Furthermore, it will be seen hereinafter that the novel process ofsurface curvature manipulation for the exit surface of the lens would beequally applicable to the input surface as well.

Referring again to FIG. 4 it will be seen that the design of thelenticular output surface of the present invention commences with thecircular arc surface segments previously discussed. A set of ten rays inthe source beam spaced evenly over the beam radius was then tracedthrough the beam spread lens of the invention. A graph was thenconstructed illustrating the relationship between the angle of thetraced ten rays in the output field of the lens as a function of the rayintercept point at the exiting surface expressed in distance from theconcave or convex axis of the lenticular pair depending upon whichportion of the contour is being designed. This curve is plotted as curve1 in FIG. 5. As can be seen from FIG. 5, curve 1, which is therelationship between the output angle of each ray and the distance fromthe axis of the lens, this relationship is nearly linear as seen bycomparing curve 1 with the dotted straight line adjacent to it in FIG.5. As previously indicated, in order to achieve the requirements for theline lens of the present invention it was deemed necessary to modify theoptical characteristics of the circular arc output surface so that therays in the output field are progressively crowded away from the axestoward the boundaries. In order to achieve this in terms of FIG. 5 it isnecessary to alter the ray-to-ray angular spacing so that in effect, therays are closer together towards the boundary of the output field. Inorder to achieve this, curve 2 in FIG. 5 was drawn empirically toprovide a smooth transition from ray-to-ray with the angular ray spacingaltered so that it is only 1/6 as great as that of curve 1 in the regionbetween 43 degrees and 45 degrees as compared to the spacing of raysnear the axis between 0 degrees and 12 degrees. The ratio 1/6 was aninitial estimate of what it would take to bring the energy density up tothe required levels as the output field approaches the 45 degreeboundary.

The method of determining the actual curvature of the output lenticularsurface to achieve the desired shift of beam rays toward the 45 degreeboundary will be discussed more fully hereinafter. However, beforedescribing this procedure it is to be noted that in design of theparticular embodiment herein disclosed, a lens having the lenticularcurvature corresponding to the ray-to-ray spacing characteristics ofcurve 2 of FIG. 5 was tested and found to be not sufficient to achievethe required characteristics. Accordingly, curve 2 was modified toprovide an even smaller ratio of ray-to-ray spacing between 43 and 45degrees as compared to the range of 0 to 12 degrees. A curve (not shown)finally used had a boundary ray to axis ray spacing ratio ofapproximately 1 to 7.

The method of determining the actual contour of the exit surface of thelens will now be described in conjunction with FIG. 6. In FIG. 6, thetop curve is derived from curve 3 of FIG. 5 and represents the tangentof the slope angles of the desired contour as a function of the distancefrom an axis of the lens. It will also be understood that because thetop curve of FIG. 6 is a graph of the tangent of the slope angles of thelens surface, the equation describing the top curve of FIG. 6 definesthe first derivature of the curve of the actual lens surface. Therefore,to generate the actual lens surface it is only necessary to perform anintegration process of the top curve to produce the final curve of therefracting surface. In the present example, this integration process wasachieved by first generating the equation for the top curve of FIG. 6.In an embodiment of this invention this equation was generated from thenumerical values by utilizing a generally available computerized curvefitting program. This equation is defined immediately below the topcurve of FIG. 6 with the constants of the resultant polynomial definedin the upper left-hand corner of FIG. 6. The bottom curve of FIG. 6represents the integral of the top curve with the integration processbeing performed along the coordinate axis.

It is recognized that the integration process would be somewhat moreaccurate if it were performed along the final curve itself instead ofalong the coordinate axis. However, the integration error is trivialparticularly in view of further empirical modificatiions that may beperformed after the lens if complete and tested.

The equation of the bottom curve of FIG. 6 therefore represents theequation for the surface contour of the lenticulated exit surface of thelens of the invention along the concave portion thereof between points Oand P as shown in FIG. 4. It will be understood that the curve for theconvex portion is obtained in the same manner as described above. Thevarious constants of the polynomial of the equation of the bottom curveof FIG. 6 are shown in the lower right-hand corner of that figure whereY and Z are SAG values indicated more specifically in Table I herein.The SAG values for the circular contoured input surface of the lens arelisted in Table II and FIG. 7 provides an explanation of the SAG valuecoordinates for both surfaces over a single lenticulation cycle. Thefinalized complete structure of the lens embodiment described herein, isillustrated in two views of FIGS. 8 and 9.

Based on the above description of the design method of the presentinvention, it will be apparent that once it has been determined whethera double power surface for such a lens is necessary and mathematicallysimple contours have been preliminarily selected for the lenticulationsfor one or both surfaces of such a lens, the design method of thepresent invention proceeds as follows:

                  TABLE I                                                         ______________________________________                                        SAG TABLE FOR POLYNOMIAL ARC                                                  CONTOURS (EXITING SURFACE)                                                            Y    Z                                                                ______________________________________                                                .040 .02102                                                                   .039 .02094                                                                   .038 .02071                                                                   .037 .02036                                                                   .036 .01992                                                                   .035 .0194                                                                    .034 .01883                                                                   .033 .01822                                                                   .032 .01759                                                                   .031 .01694                                                                   .030 .01628                                                                   .029 .01563                                                                   .028 .01500                                                                   .027 .01433                                                                   .026 .01369                                                                   .025 .01305                                                                   .024 .01241                                                                   .023 .01177                                                                   .022 .01112                                                                   .021 .01047                                                                   .020 .00982                                                                   .019 .00916                                                                   .018 .00851                                                                   .017 .00785                                                                   .016 .00720                                                                   .015 .00655                                                                   .014 .00591                                                                   .013 .00528                                                                   .012 .00466                                                                   .011 .00405                                                                   .010 .00347                                                                   .009 .00291                                                                   .008 .00238                                                                   .007 .00189                                                                   .006 .00143                                                                   .005 .00103                                                                   .004 .00068                                                                   .003 .00039                                                                   .002 .00017                                                                   .001 .00004                                                           ______________________________________                                    

                  TABLE II                                                        ______________________________________                                        SAG TABLE FOR CIRCULAR ARC                                                    CONTOURS (ENTRANCE SURFACE)                                                           Y    Z                                                                ______________________________________                                                .040 .00668                                                                   .039 .00667                                                                   .038 .00664                                                                   .037 .00660                                                                   .036 .00654                                                                   .035 .00647                                                                   .034 .00639                                                                   .033 .00630                                                                   .032 .00619                                                                   .031 .00607                                                                   .030 .00594                                                                   .029 .00579                                                                   .028 .00563                                                                   .027 .00546                                                                   .026 .00527                                                                   .025 .00507                                                                   .024 .00486                                                                   .023 .00463                                                                   .022 .00439                                                                   .021 .00414                                                                   .020 .00387                                                                   .019 .00359                                                                   .018 .00330                                                                   .017 .00291                                                                   .016 .00266                                                                   .015 .00230                                                                   .014 .00197                                                                   .013 .00168                                                                   .012 .00140                                                                   .011 .00116                                                                   .010 .00093                                                                   .009 .00074                                                                   .008 .00056                                                                   .007 .00041                                                                   .006 .00029                                                                   .005 .00018                                                                   .004 .00010                                                                   .003 .00005                                                                   .002 .00001                                                                   .001 .000                                                             ______________________________________                                    

1. Determining the output angles of incident rays as a function of thedistance along the exiting surface perpendicular to the axis of the lensfor either the convex or concave contours;

2. From the aforementioned determination of output angles, nextdetermining the ray spacing characteristics of the preliminary contoursand particularly, how the ray spacing characteristics should be alteredto change the energy distribution of the output radiation pattern toprovide a new intensity variation in the output pattern which conformsto the desired specification. For example, in the embodiment of theinvention described herein, it was found necessary to substantiallydecrease the ray spacing at angles in the output intensity patternapproaching the maximum desired limits of the beam spread wedge so thatthe ratio of angle spacing in this outer angle region of the wedge ascompared to the angle spacing out or near the axis of a lenticulationcycle, would be considerably reduced;

3. Determining by empirical methods the curve representing the alteredray spacing characteristics to produce the desired new intensitypattern. Using this equation, then deriving the curve of the tangents ofthe slope angles of the lens surface as a function of the distance fromthe axis of the lenticulations, which is then converted to mathematicalequation form by established curve fitting techniques; 4. Integratingthe previously defined equation to generate an equation of the actualaltered lens surface which will produce the altered ray spacingfunction;

5. Repeating the process for the remaining contours (concave or convex)of the output lens surface and as necessary, for the input lens surfaceas well, if required; and

6. Constructing a lens having one or more lenticulated surfaces asdefined by the aforementioned steps.

Those having skill in the pertinent art will appreciate that the lastlisted step above, namely, constructing the lens in accordance with thealtered equation of the lens surface is not a simple matter. In fact, aunique process has been employed to carry out such construction and thisprocess shall now be described in sufficient detail to enable thoseskilled in the art to construct the lens upon the completion of thedesign in accordance with the invention. Reference will be made to FIGS.10 to 13 which illustrate various apparatus used in the novel process ofmanufacture herein described.

More specifically, referring first to FIG. 10 it will be seen that inconstructing the lens of the present invention, a lens plate 20comprising a rectangular section of the applicable material, ZERODUR inthe case of the embodiment herein disclosed, is affixed to a rectangularmetal plate 22 which permits the lens material section to be handledprecisely and accurately during the steps of the construction process.The actual construction process begins on a milling machine utilizing adiamond-coated generating wheel 24 illustrated in FIG. 10. Generatingwheel 24 is a metal cylinder designed to be secured to the horizontalturret of the milling machine. The outer surface of the metal cylinderis clad with a fine grain diamond chip cylinder that has been previouslyshaped to provide a rough contour which is the obverse of the calculatedlenticulated curve surface contour of the previously described design.The generating wheel is rotated on the milling machine and compressivelyengages the lens plate 20 to produce a rough replication of the desiredcontour on the previously flat lens plate surface. The milling machineis provided with a horizontal power feed which permits the generatingwheel to move linearly in a reciprocating motion along the lens plate.Eventually the entire surface of plate 20 is homogeneously contoured bygenerating wheel 24 to achieve a rough shape closely approximating thedesired surface lenticulations for one surface of the lens. Where theopposite surface of the lens is to be contoured, lens plate 20 is turnedover and a second generating wheel is employed.

When this first step in the process has been completed, the lens plateis removed from the milling machine and secured in a lapping machine 26shown in FIG. 11. The lapping machine serves to grind and polish lensplate 20 by again utilizing a reciprocating linear motion to drive agrinding fixture 30 which is in constant compressive engagement with thelens plate. The grinding fixture is illustrated in FIG. 12. The grindingfixture typically comprises a metal material such as brass which hasbeen carefully machined to provide a grinding surface which is theobverse of the surface contour desired to be imparted to the lens. Anumber of such grinding fixtures may be provided, each having adifferent graded surface texture to permit a gradual decrease of thecoarseness of the grinding surface. Those having skill in the art towhich the machining process of the invention pertains, will appreciatethat over a period of time, after being used to manufacture numerouslenses, the grinding fixture will begin to wear and that such wear wouldotherwise inadvertently alter the surface contour of the lenses beingproduced. Accordingly, a master grinding fixture is typically providedfrom a material such as cast iron. This cast iron master fixture isprovided with a surface contour that is generated on an electronicdischarge machine to precisely match the SAG values of the desired lenscontour surface. Then the master grinding fixture is periodicallyapplied to the grinding fixture 30 to restore the grinding surface ofthe grinding fixture as required to assure lens lenticulation contourswhich very closely match the design figures previously described.

After the grinding process has been completed, the grinding fixture isreplaced in the lapping machine by a polishing fixture which is ofsimilar shape but which has a pitch polishing substrate that has beenshaped by compressive engagement with the master grinding fixture. Apolishing compound, such as Cerium oxide, is applied to the pitchpolishing substrate and the lapping machine is then employed in the samemanner to compressively engage the polishing fixture and the lens platein a constant, linearly reciprocating motion to finely polish the lenssurface.

Upon completion of the polishing step, the lens plate 20 is thenoptically tested to determine whether all the various portions of thelens plate structure have been properly surfaced to achieve the desiredoptical characteristics. If the lens plate proves satisfactory in test,the plate is then cut into appropriately shaped sections by a saw bar.If necessary, an edge machine is then used to produce the desired lensshape which as previously indicated in conjunction with FIGS. 8 and 9,is circular in the embodiment disclosed. Each cut lens is thereaftertested again for a final determination of whether or not the finishedlens product satisfies the radiation pattern specifications that havebeen established for that lens.

It will be understood that where both surfaces of the lens are to belenticulated to achieve for example, the lens structure of theparticular embodiment disclosed herein, each step of the processprovides for application of surface contouring on both sides of the lensbefore the next step in the process is commenced. Thus, for example,where both sides of the lens are to be contoured to differing shapes,two diamond generating wheels are utilized in sequence. The first isused to generate the rough lenticulation shape of one surface of thelens. Then the lens plate is removed from the lens plate fixture, turnedupside down and resecured to the fixture. The milling machine is thenused with the second generating wheel to produce the rough surface ofthe opposite side of the lens plate. Similarly, the grinding andpolishing steps of the process are applied alternatively to each side ofthe lens plate using the appropriate contoured fixture surfaces asappropriate for each lenticulation shape for the opposing sides of thelens.

It will now be understood that what has been disclosed herein comprisesan improved line lens or beam spreader lens, a novel method of designingsuch a lens and a method of manufacturing such a lens. The lens convertsa narrow, collimated round beam of radiation into a uniformlydistributed sheet of radiation utilizing at least one lenticulatedsurface. A similar lens in the prior art achieves the desired outputsheet of radiation over a 90 degree wedge generating a substantiallyuniform radiation pattern, but requires the use of a high index ofrefraction material such as LASF9 which has an index of refraction of1.85. This material however suffers the disadvantage of being opticallydegraded with increasing temperature. This is a common problemencountered in many of the applications in which the lens is utilized.Accordingly, the present invention comprises such a lens using amaterial of substantially lower index of refraction such as glassceramic but which is relatively insensitive to heat effects. The presentinvention also comprises a unique design method for calculating thecontour surfaces of such a lens, and a novel means for producing a lensstructure which satisfies the optical specifications of prior artdevices but which does so utilizing a lens material having asubstantially reduced index of refraction, namely, having an index ofrefraction of less than 1.6.

The invention herein disclosed comprises a novel design method forcalculating the contours of a lenticulated surface to redistribute theoptical energy in a beam spreader lens to achieve a desired intensitypattern. The novel design method disclosed herein has been applied to aspecific embodiment of a lens structure of the invention to enable thosehaving ordinary skill in the art to which the invention pertains toutilize that design method to achieve surface contours for any desiredradiation pattern in a beam spreader lens. A novel method of manufacturefor constructing such a uniquely designed lenticulated surface line lenshas also been disclosed herein.

It will be understood that the specific embodiment of the line lensherein disclosed provides only one exemplary illustration for applyingthe design method of the invention and that virtually an unlimitednumber of other surface contour combinations achieve the desiredradiation pattern specifications can be utilized as a result of thedesign method herein disclosed. As a result of the teaching herein, itwill now be apparent that numerous modifications and additions may bemade to the invention herein disclosed, however all such modificationsand additions are contemplated as being within the scope of theinvention which is to be limited only by the claims appended hereto.

I claim:
 1. A lens apparatus of the type receiving a collimated beam ofinput radiation for transmitting a narrow sheet of output radiation ofsubstantially uniform intensity over an angular range of approximately +and -45 degrees relative to the input radiation beam; the apparatuscomprising:an optically transparent material having an index ofrefraction no greater than 1.6 and having; a lenticulated receivingsurface; and a lenticulated transmitting surface; wherein thelenticulated contours of said lenticulated receiving surface arealternately convex and concave, the convex contours being wider than theconcave contours.
 2. The lens apparatus recited in claim 1 wherein thelenticulated contours of said lenticulated transmitting surface arealternately convex and concave, the concave contours being wider thanthe convex contours.
 3. The lens apparatus recited in claim 2 whereinthe lenticulation contours of said lenticulated receiving surface arecircular and the lenticulated contours of said lenticulated transmittingsurface are non-circular.
 4. The lens apparatus recited in claim 3wherein the contours of said transmitting surface may be described by afifth degree polynomial equation.
 5. The lens apparatus recited in claim3 wherein the concave contours of said transmitting surface aregeometrically similar to the convex contours of said transmittingsurface.
 6. The lens apparatus recited in claim 2 wherein the convexcontours of the respective surfaces share a common axis plane andwherein the concave contours of the respective surfaces share a commonaxis plane, said axis planes being parallel to each other.
 7. A methodof constructing a lens, the lens of the type receiving a collimated beamof input radiation for transmitting a narrow sheet of output radiationof substantially uniform intensity over an angular range of at leastapproximately + and -45 degrees relative to the input radiation beam;the method comprising the following steps:a. selecting the number oflens surfaces that will be required to affect the incoming radiationbeam for a given transmissive material, b. providing each surfaceselected in step a. with lenticulations comprising alternating convexand concave elements having mathematically simple contours such ascircular arcs, c. determining the output radiation angles of incidentbeam rays as a function of the distance along the exiting surface of alenticulation element, d. modifying the output radiation angle spacingdetermined in step c. to achieve a desired output radiation intensitypattern as a function of angle relative to the input radiation beam, e.determining the curve representing the altered output radiation spacing,f. deriving the mathematical equation of the curve of the tangents ofthe slope angles of the lens surface as a function of the distance fromthe axis of the lenticulation element, g. integrating the equationdetermined in step f. to generate the equation of the lens surfaceelement contour which provides the altered output radiation spacing, h.repeating steps c. through g. for each additional lens surface elementcontour which must be also altered to achieve the desired outputradiation pattern for the entire lens, i. defining the entire lensgeometry in accordance with the results of steps a. through h, and j.constructing a lens having the geometry defined in step i.
 8. A methodof constructing a lens, the lens of the type receiving a collimated beamof input radiation for transmitting a prescribed pattern of outputradiation of selected intensity and shape, the method comprising thesteps of:a. selecting the number of lens surfaces that will be requiredto affect the incoming radiation beam for a given transmissive material,b. providing each surface selected in step a. with lenticulationscomprising alternating convex and concave elements having mathematicallysimple contours such as circular arcs, c. determining the outputradiation angles of incident beam rays as a function of the distancealong the exiting surface of a lenticulation element, d. modifying theoutput radiation angle spacing determined in step c. to achieve adesired output radiation intensity pattern as a function of anglerelative to the input radiation beam, e. determining the curverepresenting the altered output radiation spacing, f. deriving themathematical equation of the curve of the tangents of the slope anglesof the lens surface as a function of the distance from the axis of thelenticulation element, g. integrating the equation determined in step f.to generate the equation of the lens surface element contour whichprovides the altered output radiation spacing, h. repeating steps c.through g. for each additional lens surface element contour which mustbe also altered to achieve the desired output radiation pattern for theentire lens, i. defining the entire lens geometry in accordance with theresults of steps a. through h, and j. constructing a lens having thegeometry defined in step i.